Torsion orders of complete intersections

Chatzistamatiou, Andre; Levine, Marc

doi:10.2140/ant.2017.11.1779

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Torsion orders of complete intersections

Andre Chatzistamatiou and Marc Levine

Vol. 11 (2017), No. 8, 1779–1835

DOI: 10.2140/ant.2017.11.1779

Abstract

By a classical method due to Roitman, a complete intersection $X$ of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer $N$ , when viewed as a cycle in the Chow group, has support in $X \times D \cup F \times X$ , for some divisor $D$ and a finite set of closed points $F$ . The minimal such $N$ is called the torsion order. We study lower bounds for the torsion order following the specialization method of Voisin, Colliot-Thélène, and Pirutka. We give a lower bound for the generic complete intersection with and without point. Moreover, we use methods of Kollár and Totaro to exhibit lower bounds for the very general complete intersection.

Keywords

algebraic cycles, decomposition of the diagonal

Mathematical Subject Classification 2010

Primary: 14C25

Milestones

Received: 23 May 2016

Revised: 14 June 2017

Accepted: 29 July 2017

Published: 15 October 2017

Authors

Andre Chatzistamatiou
Fakultät Mathematik Universität Duisburg-Essen Essen Germany

Marc Levine
Fakultät Mathematik Universität Duisburg-Essen Essen Germany

Vol. 11, No. 8, 2017